"... Free space Green�s functions are derived for graded materials in which the thermal conductivity varies exponentially in one coordinate. Closed form expressions are obtained for the steady state di�usion equation � in two and three dimensions. The corresponding boundary integral equation formula� tio ..."

Free space Green�s functions are derived for graded materials in which the thermal conductivity varies exponentially in one coordinate. Closed form expressions are obtained for the steady state di�usion equation � in two and three dimensions. The corresponding boundary integral equation formula� tions for these problems are derived � and the three�dimensional case is solved numerically using a Galerkin approximation. The results of test calculations are in excellent agreement with exact solutions and �nite element simula� tions. Key words. Green�s functions � functionally graded materials � di�usion� boundary integral analysis � Galerkin approximation. Abbreviated title � Green�s functions for FGMs 1